The efficiency of turbomachines, in particular of gas turbines, can be increased by increasing the cyclic process parameters of the turbomachine. In this case, the relevant cyclic process parameters are the pressure and the temperature of the fluid. The fluid temperatures normally occurring nowadays during the operation of turbomachines, in particular in the turbine inlet region, are already markedly above the admissible material temperatures of the components. In this case, in particular the components forming the flow passage or projecting into the flow passage are directly exposed to the hot fluid flow. As a rule, the heat dissipation of the components, which is brought about by the heat conduction of the material, is not sufficient here in order to avoid an excess temperature of the components. Material temperatures which are too high first of all lead to a drop in the strength values of the material. In the process, crack formation often occurs in the components. In addition, in the event of the melting temperature of the material being exceeded, local or even complete destruction of the component occurs. In order to avoid these fatal consequences, care has to be taken in order to ensure that the component temperatures do not exceed the maximum admissible material temperatures. The flow passage of a turbomachine is often composed of platforms set side by side in an annular manner. The blades of turbomachines are often arranged on such platforms. One blade each is usually made in one piece with one platform. In particular in the case of stators, however, such platforms are often arranged in the form of a shroud of the blading on the blade tips. These platforms are therefore directly exposed to the hot fluid flow. In order not to exceed the maximum admissible material temperature of the platforms, the aim hitherto was normally to achieve over the passage height a temperature profile of the fluid, usually air, discharging from the combustion chamber, in the turbine inlet region. This temperature profile could be achieved via an admixture of cooling fluid into the marginal regions of the hot fluid flow in the discharge region of the combustion chamber. The fluid directly adjacent to the side walls and thus to the platforms, compared with the temperature of the core flow, therefore had a markedly reduced temperature. An excess temperature of the platforms could thus be avoided. On the one hand, a fluid-flow energy content varying over the passage height turns out to be a disadvantage of this method. This fluid-flow energy content varying over the passage height leads in turn to a non-uniform energy conversion in a following rotor and thus to non-uniform loading of the blading over the passage height. Resulting as a further disadvantage of this admixing of cooling fluid to the main flow is a reduction in the efficiency achievable and thus also a reduction in the power density of the turbomachine. For these reasons, a uniform temperature profile over the passage height is aimed at nowadays. In addition, modern combustion chambers are nowadays designed from the aspect of NO.sub.x reduction in such a way that admixing of secondary combustion air is no longer effected or only slight admixing of secondary combustion air is effected. This results in a very uniform temperature profile over the passage height. This in turn leads to an increase in the thermal loading of the components which are arranged downstream of the combustion chamber, in particular of the side walls and thus of the platforms. Here, it has hitherto been attempted to cool the platforms by blowing out a cooling fluid mostly directly upstream of the platforms. In this case, the cooling fluid is intended to form a cooling film on the top side of the platforms, as a result of which a fluidic separation between the hot fluid and the respective platform occurs. However, the effect of such cooling films, on account of the intermixing with the hot gas, is often quite restricted spatially. Changing pressure conditions of the hot-gas flow or even of the cooling fluid over the load range of a turbomachine likewise lead to a changed cooling film. In addition, in order to ensure adequate cooling, a relatively large cooling-fluid mass flow is required. This in turn leads to a reduction in the efficiency of the turbomachine.